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## Official Guide Explanation:Problem Solving #151

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 151
Page: 82
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Counting Methods > Combinations

Explanation: This is a combinations question. There are 7 possible selections of 1 person from a group of 7 candidates for the math position. The number of selections for the computer science positions is trickier. To find the number of possibilities of 2 selections from 10 candidates, use the combinations formula:

c = ((n!)/(k!(n - k)!)) = ((10!)/(2!8!)) = ((10(9))/2) = 45

Since there are 7 possibilities for the math position and 45 for the comp sci positions, the total number of sets is the product:

7(45) = 315, choice (E).

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